I’ve recently had to do some job hunting. Before I had to leave my current job, I had been looking and even had a couple of really great interviews! I never once offered or included my references. I, like you, did not want to jeopardize my position. You should still apply to whatever interests you. If you get any calls and are asked for an interview, then make sure you have your references. I found that most employers don’t need references ASAP, and some depending on your interview, won’t even ask for them. If they absolutely require you to apply with references, just add that you’ll give them upon request at the interview. It is your private information in regards to whom you would like to give you the best feedback when your supplying a name for a reference. Are they wanting to call before the interview is done, or is it just the standard after the interview? If someone really wants you to work for them, they won’t push you away with threats.